arXiv subjects

Anirvan DasGupta

Publications and source records attributed to Anirvan DasGupta.

3 recordsLinked to original sources

arXiv2015

Evolution of geodesic congruences in a gravitationally collapsing scalar field background

The evolution of timelike geodesic congruences in a spherically symmetric, nonstatic, inhomogeneous spacetime representing gravitational collapse of a massless scalar field is studied. We delineate how initial values of the expansion, rotation and shear of a congruence, as well as the spacetime curvature, influence the global behavior and focusing properties of a family of trajectories. Under specific conditions, the expansion scalar is shown to exhibit a finite jump (from negative to positive value) before focusing eventually occurs. This nonmonotonic behavior of the expansion, observed in our numerical work, is successfully explained through an analysis of the equation for the expansion. Finally, we bring out the role of the metric parameters (related to nonstaticity and spatial inhomogeneity), in shaping the overall behavior of geodesic congruences.

gr-qc↗

arXiv2014

Kinematics of trajectories in classical mechanics

In this paper, we show how the study of kinematics of a family of trajectories of a classical mechanical system may be unified within the framework of analysis of geodesic flows in Riemannian geometry and Relativity. After setting up the general formalism, we explore it through studies on various one and two dimensional systems. Quantities like expansion, shear and rotation (ESR), which are more familiar to the relativist, now re-appear while studying such families of trajectories in configuration space, in very simple mechanical systems. The convergence/divergence of a family of trajectories during the course of time evolution, the shear and twist of the area enclosing the family, and the focusing/defocusing of the trajectories within a finite time are investigated analytically for these systems. The understanding of the configuration space developed through such investigations is elaborated upon, and possible future avenues are pointed out.

gr-qc↗

arXiv2012

Geodesic flows in rotating black hole backgrounds

We study the kinematics of timelike geodesic congruences, in the spacetime geometry of rotating black holes in three (the BTZ) and four (the Kerr) dimensions. The evolution (Raychaudhuri) equations for the expansion, shear and rotation along geodesic flows in such spacetimes are obtained. For the BTZ case, the equations are solved analytically. The effect of the negative cosmological constant on the evolution of the expansion ($θ$), for congruences with and without an initial rotation ($ω_0$) is noted. Subsequently, the evolution equations, in the case of a Kerr black hole in four dimensions are written and solved numerically, for some specific geodesics flows. It turns out that, for the Kerr black hole, there exists a critical value of the initial expansion below (above) which we have focusing (defocusing). We delineate the dependencies of the expansion, on the black hole angular momentum parameter, $a$, as well as on $ω_0$. Further, the role of $a$ and $ω_0$ on the time (affine parameter) of approach to a singularity (defocusing/focusing) is studied. While the role of $ω_0$ on this time of approach is as expected, the effect of $a$ leads to an interesting new result.

gr-qc↗